Determination of high‐order fields for multianisotropic material antiplane V‐notches and inclusions by the asymptotic expansion technique and an overdeterministic method

Abstract

In this paper, the singular behavior for anisotropic multimaterial V-notched plates is investigated under antiplane shear loading condition. Firstly, the elastic governing equations are transformed into eigen ordinary differential equations through introducing the asymptotic expansions of displacements near the notch tip. The stress singularity exponents, including the higher-order terms, and the corresponding eigen angular functions are then obtained by solving the established equations by using the interpolating matrix method.Thus, using the combination of the results from finite element analyses and the derived asymptotic expansion, an overdeterministic method is employed to calculate the amplitudes of the coefficients in the asymptotic expansions.Finally, the stress and displacement fields in the vicinity of the notch tip, consisting of both singular terms and higher-order terms, are determined.The effects of material properties and geometry characteristic on the singular behaviour of the notch tip are discussed in detail. K E Y W O R D Santiplane V-notch, eigen analysis, finite element method, higher-order terms, multimaterial

Crack tip fields in anisotropic planes: a review

“…crack tip coefficients) so as to have an over-determined system of displacement equations. Treating such problem with the least squares scheme will finally output the sought-after crack tip parameters (Ayatollahi and Nejati 2011;Ayatollahi et al 2020;Yao et al 2020a). • Extended finite element method (XFEM): Another well-known FEM-based approach is the extended finite element method which utilises enriched shape functions for elements at the crack tip.…”

On the effects of higher order stress terms in pure mode III loading of bi‐material notches

“…Subsequently, by forming a determined system of equations, they computed the coefficients of the functions. Moreover, the same method has been employed by Yao et al 25 to evaluate coefficients of the stress series expansion except that instead of using a determined system of equations, they utilized the over‐deterministic method. One of the drawbacks of this method is the utilization of numerical estimations in every step of calculations, which increases the cost of computations and may cause significant errors in the final results.…”